Radio device with resonator

A radio device 110 comprises a radio transceiver 105 & 107, a resonator 101, a temperature measurement unit 102, a frequency synthesiser 113 and a processing system 104. A signal from the temperature measurement unit, representative of a measured temperature of the resonator, is used to determine an estimated frequency offset Fest for the resonator at the measured temperature using a model, stored in a memory of the processing system, that relates frequency offset to temperature. A periodic signal fr from the resonator is provided to the frequency synthesizer, which, in dependence on the estimated frequency offset Fest, is used to generate a periodic local signal used as a local oscillator signal for transmitting a first radio signal from the transceiver. The transceiver receives a second radio signal comprising a periodic component at a stable, received signal frequency. An error value representative of a difference between the received signal frequency and a frequency of the periodic local signal is determined and used to update one or more parameters of the model stored in the memory. The system finds particular application with half-duplex radio links, e.g. NB-IoT and eMTC, in which transmit and receive operations are carried out at different times.